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Yes, FF are allowed.  Pretty sure just about everyone uses some sort of FF handguard.  And as far as the trigger goes, for Service Rifle you can use a trigger of at least 4.5 lbs. 6 is a bit heavy.

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Yes, not only are you allowed to have a free float hand guard, it's the standard for high power rifle. I shoot these matches and I've never seen a non-free-floated AR15 there. Maybe some of the old garands and M14s are bedded instead of free floated. I shoot the Rock River national match A4. Link is here:
https://www.rockriverarms.com/index.cfm?fuseaction=category.display&category_ID=252

It has a float tube concealed under the handguards. You can't tell from the product photo, but look at one up close and the sling attachment point is totally isolated from the barrel. So no matter what position you are in with your sling, there's no pressure on the barrel from it. It would be quite a disadvantage to not have that.

I have the RR two-stage 4.5 lb trigger in my rifle and it works well. I shot a match with a rifle that had a geiselle trigger in it yesterday, and it had not been broken in yet. I thought my RR trigger was better and also it cost less. Some people like the geiselle trigger better, though. Either one is good enough for competition.

You can and should absolutely use a free float handguard. There are several options:

Geiselle makes a really nice one, it should be on sale for around $265 on black friday. imo the easiest of all of them to assemble and disassemble. Buy once cry once. This ff handguard makes barrel changes and gas block removal when cleaning as easy as it gets.

White Oak Armament (Same as Rock River Nat'l match), sells for about $150 - uses a lock ring. Order some extra lock rings from RRA or WOA if you do you own assembling. You'll need them I promise.

Compass Lake Engineering (Frank White design)  the most simple design of them all. It does not use a lock ring. Alignment can be a little tricky sometimes.

Krieger also sells one. I think they are around $180. It's a 3 piece design. They have plenty in stock, but are not making any more after they sell all of these. This is the heaviest of all the free float tubes, and the strongest. It's built with very thick walled chromoly.